On Karatsuba's Problem Concerning the Divisor Function τ(n)\tau(n)

We study an asymptotic behavior of the sum \sum\limits_{n\le x}\frac{\D \tau(n)}{\D \tau(n+a)}. Here $\tau(n)$ denotes the number of divisors of $n$ and $a\ge 1$ is a fixed integer.Comment: 32 page

Fisher waves in the strong noise limit

We investigate the effects of strong number fluctuations on traveling waves in the Fisher-Kolmogorov reaction-diffusion system. Our findings are in stark contrast to the commonly used deterministic and weak-noise approximations. We compute the wave velocity in one and two spatial dimensions, for which we find a linear and a square-root dependence of the speed on the particle density. Instead of smooth sigmoidal wave profiles, we observe fronts composed of a few rugged kinks that diffuse, annihilate, and rarely branch; this dynamics leads to power-law tails in the distribution of the front sizes.Comment: 4 pages, 2 figures, updat

A modular cloning toolkit for genome editing in plants

Background CRISPR/Cas has recently become a widely used genome editing tool in various organisms, including plants. Applying CRISPR/Cas often requires delivering multiple expression units into plant and hence there is a need for a quick and easy cloning procedure. The modular cloning (MoClo), based on the Golden Gate (GG) method, has enabled development of cloning systems with standardised genetic parts, e.g. promoters, coding sequences or terminators, that can be easily interchanged and assembled into expression units, which in their own turn can be further assembled into higher order multigene constructs. Results Here we present an expanded cloning toolkit that contains 103 modules encoding a variety of CRISPR/Cas-based nucleases and their corresponding guide RNA backbones. Among other components, the toolkit includes a number of promoters that allow expression of CRISPR/Cas nucleases (or any other coding sequences) and their guide RNAs in monocots and dicots. As part of the toolkit, we present a set of modules that enable quick and facile assembly of tRNA-sgRNA polycistronic units without a PCR step involved. We also demonstrate that our tRNA-sgRNA system is functional in wheat protoplasts. Conclusions We believe the presented CRISPR/Cas toolkit is a great resource that will contribute towards wider adoption of the CRISPR/Cas genome editing technology and modular cloning by researchers across the plant science community

Photon Filamentation in Resonant Media with High Fresnel Numbers

The phenomenon of turbulent photon filamentation occurs in lasers and other active optical media at high Fresnel numbers. A description of this phenomenon is suggested. The solutions to evolution equations are presented in the form of a bunch of filaments chaotically distributed in space and having different radii. The probability distribution of patterns is defined characterizing the probabilistic weight of different filaments. The most probable filament radius and filament number are found, being in good agreement with experiment.Comment: Revtex file, 5 pages. Reference to the English edition of the journal is give

Unconventional magnetism of non-uniform distribution of Co in TiO2 nanoparticles

High-resolution transmission electron microscopy (HRTEM), X-ray diffraction (XRD) analysis, electron paramagnetic resonance (EPR), X-ray absorption spectroscopy (XAS), magnetic methods, and density-functional theory (DFT) calculations were applied for the investigations of Co-doped anatase TiO2 nanoparticles (∼20 nm). It was found that high-spin Co2+ ions prefer to occupy the interstitial positions in the TiO2 lattice which are the most energetically favourable in compare to the substitutional those. A quantum mechanical model which operates mainly on two types of Co2+ – Co2+ dimers with different negative exchange interactions and the non-interacting paramagnetic Co2+ ions provides a satisfactorily description of magnetic properties for the TiO2:Co system. © 2020 Elsevier B.V.Russian Foundation for Basic Research. Ministry of Science and Higher Education of the Russian Federatio

Velocity and processivity of helicase unwinding of double-stranded nucleic acids

Helicases are molecular motors which unwind double-stranded nucleic acids (dsNA) in cells. Many helicases move with directional bias on single-stranded (ss) nucleic acids, and couple their directional translocation to strand separation. A model of the coupling between translocation and unwinding uses an interaction potential to represent passive and active helicase mechanisms. A passive helicase must wait for thermal fluctuations to open dsNA base pairs before it can advance and inhibit NA closing. An active helicase directly destabilizes dsNA base pairs, accelerating the opening rate. Here we extend this model to include helicase unbinding from the nucleic-acid strand. The helicase processivity depends on the form of the interaction potential. A passive helicase has a mean attachment time which does not change between ss translocation and ds unwinding, while an active helicase in general shows a decrease in attachment time during unwinding relative to ss translocation. In addition, we describe how helicase unwinding velocity and processivity vary if the base-pair binding free energy is changed.Comment: To appear in special issue on molecular motors, Journal of Physics - Condensed Matte

High Ice Water Content at Low Radar Reflectivity near Deep Convection: Part II. Evaluation of Microphysical Pathways in Updraft Parcel Simulations

The aeronautics industry has established that a threat to aircraft is posed by atmospheric conditions of substantial ice water content (IWC) where equivalent radar reflectivity (Ze) does not exceed 20-30 dBZ and supercooled water is not present; these conditions are encountered almost exclusively in the vicinity of deep convection. Part 1 (Fridlind et al., 2015) of this two-part study presents in situ measurements of such conditions sampled by Airbus in three tropical regions, commonly near 11 km and -43 C, and concludes that the measured ice particle size distributions are broadly consistent with past literature with profiling radar measurements of Z(sub e) and mean Doppler velocity obtained within monsoonal deep convection in one of the regions sampled. In all three regions, the Airbus measurements generally indicate variable IWC that often exceeds 2 gm (exp -3) with relatively uniform mass median area-equivalent diameter (MMD(sub eq) of 200-300 micrometers. Here we use a parcel model with size-resolved microphysics to investigate microphysical pathways that could lead to such conditions. Our simulations indicate that homogeneous freezing of water drops produces a much smaller ice MMD(sub eq) than observed, and occurs only in the absence of hydrometeor gravitational collection for the conditions considered. Development of a mass mode of ice aloft that overlaps with the measurements requires a substantial source of small ice particles at temperatures of about -10 C or warmer, which subsequently grow from water vapor. One conceivable source in our simulation framework is Hallett-Mossop ice production; another is abundant concentrations of heterogeneous ice freezing nuclei acting together with copious shattering of water drops upon freezing. Regardless of the production mechanism, the dominant mass modal diameter of vapor-grown ice is reduced as the ice-multiplication source strength increases and as competition for water vapor increases. Both mass and modal diameter are reduced by entrainment and by increasing aerosol concentrations. Weaker updrafts lead to greater mass and larger modal diameters of vapor-grown ice, the opposite of expectations regarding lofting of larger ice particles in stronger updrafts. While stronger updrafts do loft more dense ice particles produced primarily by raindrop freezing, we find that weaker updrafts allow the warm rain process to reduce competition for diffusional growth of the less dense ice expected to persist in convective outflow

Typical sections of Bashkirian carbonate rocks and structure of oil deposits in southeast part of the Republic of Tatarstan

Carbonate rocks of Bashkirian stage are regional oil saturation in southeast part of the Republic of Tatarstan. Bashkirian reservoir rocks are not all oil saturation that is caused by environments of carbonate sedimentation. We suggest sedimentation scheme and typical lithological sections of Bashkirian layers. Lithological typification and reconstruction of sedimentation carbonate rocks allows to prospecting oil reservoir. Reservoir type of limestone irregularly detect in Bashkirian sequences. They can form massive and multilayer oil reservoir. Often, section absent reservoir limestone, so this section non perspective for oil development

Skyrmionic excitons

We investigate the properties of a Skyrmionic exciton consisting of a negatively charged Skyrmion bound to a mobile valence hole. A variational wave function is constructed which has the generalized total momentum P as a good quantum number. It is shown that the Skyrmionic exciton can have a larger binding energy than an ordinary magnetoexciton and should therefore dominate the photoluminescence spectrum in high-mobility quantum wells and heterojunctions where the electron-hole separation exceeds a critical value. The dispersion relation for the Skyrmionic exciton is discussed.Comment: 9 pages, RevTex, 2 PostScript figures. Replaced with version to appear in Phys. Rev. B Rapid Communications. Short discussion of variational state adde

High Ice Water Content at Low Radar Reflectivity near Deep Convection

Occurrences of jet engine power loss and damage have been associated with flight through fully glaciated deep convection at -10 to -50 degrees Centigrade. Power loss events commonly occur during flight through radar reflectivity (Zeta (sub e)) less than 20-30 decibels relative to Zeta (dBZ - radar returns) and no more than moderate turbulence, often overlying moderate to heavy rain near the surface. During 2010-2012, Airbus carried out flight tests seeking to characterize the highest ice water content (IWC) in such low-radar-reflectivity regions of large, cold-topped storm systems in the vicinity of Cayenne, Darwin, and Santiago. Within the highest IWC regions encountered, at typical sampling elevations (circa 11 kilometers), the measured ice size distributions exhibit a notably narrow concentration of mass over area-equivalent diameters of 100-500 micrometers. Given substantial and poorly quantified measurement uncertainties, here we evaluate the consistency of the Airbus in situ measurements with ground-based profiling radar observations obtained under quasi-steady, heavy stratiform rain conditions in one of the Airbus-sampled locations. We find that profiler-observed radar reflectivities and mean Doppler velocities at Airbus sampling temperatures are generally consistent with those calculated from in situ size-distribution measurements. We also find that column simulations using the in situ size distributions as an upper boundary condition are generally consistent with observed profiles of radar reflectivity (Ze), mean Doppler velocity (MDV), and retrieved rain rate. The results of these consistency checks motivate an examination of the microphysical pathways that could be responsible for the observed size-distribution features in Ackerman et al. (2015)